Conventional optical devices consist mainly of shaped dielectrics and metals. The trajectories of individual rays of light are altered via refraction and reflection at the boundaries of these homogeneous materials. The traditional optical design process is therefore reduced to finding materials with better optical responses and optimizing their surface contours for various applications. Gradient-Index (GRIN) devices introduce a new degree of freedom to the design process by incorporating inhomogeneous dielectrics. Ray trajectories are no longer restricted to straight lines inside GRIN elements, and can instead be gently curved by the gradient in the index of refraction.
In some sense, Transformation Optics (TO) is a generalization of GRIN design. Instead of simply specifying a gradient in the isotropic refractive index of a material, TO yields individual gradients in all tensor components in the electrical permittivity ∈ and magnetic permeability μ. However, while traditional optical design is based on the short wavelength approximations of geometrical optics, TO is accurate to the level of the macroscopic Maxwell's equations, and has shown application even at zero frequency.
Unfortunately, like GRIN technology, the design freedom afforded by TO comes at the cost of complexity and extreme material parameters. In principle, these designs can be implemented with metamaterials (MMs)—composites that provide artificial material responses. In practice, however, metamaterials can add a host of complexities and restrictions to the design process. The complexity of the TO material prescription has continually forced researchers to make simplifying approximations in order to achieve any of the desired functionality, even when the dimensionality of the problem is reduced and the polarization is restricted.
One significant application of metamaterials is in the design and implementation of surface scattering antennas. Surface scattering antennas are described, for example, in A. Bily et al, “Surface Scattering Antennas,” U.S. Patent Application Publication No. 2012/0194399 (“Bily I”); A. Bily et al, “Surface Scattering Antenna Improvements,” U.S. Patent Application No. 2014/0266946 (“Bily II”); and P.-Y. Chen et al, “Surface Scattering Antennas with Lumped Elements,” U.S. Application No. 61/988,023 (“Chen”), each of which is herein incorporated by reference. Surface scattering antennas generally include a waveguide structure such as a coplanar waveguide, microstrip, stripline, or closed waveguide (such as a rectangular waveguide or substrate integrated waveguide), with a plurality of adjustable scattering elements coupled to and positioned along the waveguide. In some approaches the waveguide is a one-dimensional waveguide; in other approaches the waveguide is two-dimensional (as with a parallel plate waveguide or a plurality of parallel one-dimensional waveguides filling a two-dimensional antenna aperture). The adjustable scattering elements may include, for example, complementary metamaterial elements, such as CELC (complementary electric LC) or CSRR (complementary split ring resonators) structures. Complementary metamaterial elements are described, for example, in D. R. Smith et al, “Metamaterials for surfaces and waveguides,” U.S. Patent Application Publication No. 2010/0156573 (herein incorporated by reference), and further described herein. In other approaches, the scattering elements are subwavelength patches positioned above apertures in the waveguide structure. The scattering elements can be made adjustable by various approaches described, for example, in Bily I, Bily II, and Chen, infra. For example, in some approaches the scattering elements include an electrically-adjustable material such as a liquid crystal material or a ferroelectric material, and the scattering elements are then adjusted by applying an adjustable voltage across the electrically-adjustable material; in other approaches the scattering elements include lumped elements such as transistors or diodes (including varactor diodes), and the scattering elements are then adjusted by applying voltages across the terminals of the lumped elements (e.g. to vary a capacitance or switch a transistor between ohmic/saturation mode and pinch-off mode). The set of possible adjustments of the adjustable scattering elements can be a binary set of adjustments (i.e. just two possible adjustment states) or a grayscale set of adjustment (i.e. more than two possible adjustment states).
These surface scattering antennas generally use a holographic principle to define a radiation pattern of the reference antenna. The radiation pattern is determined by an interference between a reference wave, which is a guided wave that propagates along the waveguide structure, and a holographic antenna configuration, which is a modulation pattern imposed on the antenna by the adjustments of the scattering elements. The design of an antenna modulation to provide a desired radiation pattern may be complicated by coupling between the scattering elements and by interactions such that the form of the modulation perturbs the reference mode.
In view of the foregoing, it is desired to provide improved techniques and systems for TO design with metamaterials and for holographic antenna pattern designs for surface scattering antennas.